From statistics of regular tree-like graphs to distribution function and gyration radius of branched polymers

Alexander Y. Grosberg, Sergei K. Nechaev

    Research output: Contribution to journalArticle

    Abstract

    We consider flexible branched polymer, with quenched branch structure, and show that its conformational entropy as a function of its gyration radius R, at large R, obeys, in the scaling sense, ΔS ∼ R2/(a2L), with a bond length (or Kuhn segment) and L defined as an average spanning distance. We show that this estimate is valid up to at most the logarithmic correction for any tree. We do so by explicitly computing the largest eigenvalues of Kramers matrices for both regular and 'sparse' three-branched trees, uncovering on the way their peculiar mathematical properties.

    Original languageEnglish (US)
    Article number345003
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume48
    Issue number34
    DOIs
    StatePublished - Aug 6 2015

    Keywords

    • Kramers theorem
    • branched polymers
    • eigenvalue analysis

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Statistics and Probability
    • Modeling and Simulation
    • Mathematical Physics
    • Physics and Astronomy(all)

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